Optimal. Leaf size=23 \[ \frac {11}{5}+2 \left (\frac {3 (16+e)^4}{2 x}-x\right )+x \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {14} \begin {gather*} \frac {3 (16+e)^4}{x}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {3 (16+e)^4}{x^2}\right ) \, dx\\ &=\frac {3 (16+e)^4}{x}-x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 14, normalized size = 0.61 \begin {gather*} \frac {3 (16+e)^4}{x}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.51, size = 26, normalized size = 1.13 \begin {gather*} -\frac {x^{2} - 3 \, e^{4} - 192 \, e^{3} - 4608 \, e^{2} - 49152 \, e - 196608}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 25, normalized size = 1.09 \begin {gather*} -x + \frac {3 \, {\left (e^{4} + 64 \, e^{3} + 1536 \, e^{2} + 16384 \, e + 65536\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 28, normalized size = 1.22
method | result | size |
default | \(-x -\frac {-4608 \,{\mathrm e}^{2}-49152 \,{\mathrm e}-3 \,{\mathrm e}^{4}-192 \,{\mathrm e}^{3}-196608}{x}\) | \(28\) |
gosper | \(\frac {3 \,{\mathrm e}^{4}+192 \,{\mathrm e}^{3}+4608 \,{\mathrm e}^{2}-x^{2}+49152 \,{\mathrm e}+196608}{x}\) | \(34\) |
risch | \(-x +\frac {4608 \,{\mathrm e}^{2}}{x}+\frac {49152 \,{\mathrm e}}{x}+\frac {3 \,{\mathrm e}^{4}}{x}+\frac {192 \,{\mathrm e}^{3}}{x}+\frac {196608}{x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 25, normalized size = 1.09 \begin {gather*} -x + \frac {3 \, {\left (e^{4} + 64 \, e^{3} + 1536 \, e^{2} + 16384 \, e + 65536\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.78, size = 15, normalized size = 0.65 \begin {gather*} \frac {3\,{\left (\mathrm {e}+16\right )}^4}{x}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 27, normalized size = 1.17 \begin {gather*} - x - \frac {-196608 - 49152 e - 4608 e^{2} - 192 e^{3} - 3 e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________